M4209503 Mersenne number exponent details

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M4209503

<<<

>>>

is 2 ^4209503 - 1

has 1267187 decimal digits

takes 0.525 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	7.0588	65.6716%	-	-	-	-	7.0588	65.6716%	0.0000%
PrimeNet	2⁶¹	0.0730	62.2951%	17000	340000	0.0063	2.8357%	0.0792	63.3643%	1.0692%
GPU72	2⁶⁵	1.7331	64.6154%	22000	450000	0.0082	1.8756%	1.7413	65.2790%	0.6637%
Difference	+2	+5.3256	+1.0563%	-22000	-450000	-0.0082	-1.8756%	+5.3174	+0.3926%	+0.3926%

Known prime factors (2 factors, 101.9 bits, 0.00242054% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4209503	50724511151	11	35.562	6025 5² × 241	-	25	241	1.418e-9	6.649e-6	9.201e-6
4209503	92811776926803486161	20	66.331	11024077774360 2³ × 5 × 7 × 23 × 509 × 3363091	2018-12-16	509	3363091	5.0146	0.0332	0.0619

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
4209503	50724511151 92811776926803486161	4707832013667767944559318681311	31	101.893

P-1 results:
No P-1 results for M4209503

Trial Factoring results:
No TF results for M4209503

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.182 GHz-days
Estimated T-Level:	0.050

Digits	B1	Curves	Complete	FacMiss
20	11000	1 / 100	0.010	99.000%
25	50000	1 / 280	0.004	99.643%

New Calculation Method

Total ECM effort:	0.182 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.032	96.826%
25	50000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	92811776926803486161	1	0.182

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-12-17T04:52:53	MarkS	laptop64	50000	5000000	92811776926803486161	66.331	1	2		1	0.182

Lucas-Lehmer results:
No L-L results for M4209503

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T06:34:17

kkmrkkblmbrbk

Manual testing

50724511151

397E761E2BB833__

2018-01-22T11:54:27

alan145

Bear1

50724511151

397E761E2BB833__

2018-12-20T04:48:37

Luigi Morelli

GoogleCloudTmp

50724511151

92811776926803486161

CF69234CDCB6038C

2018-12-22T01:19:52

Oliver Kruse

GTX-5

50724511151

92811776926803486161

CF69234CDCB6038C

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

10⁰

10¹

10²

10³

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁶⁷

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2018-12-22T01:19:52+00:00

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront